ascending chain造句

• The Artin Wedderburn theorem generalises this result, with the ascending chain condition.
• Similarly, the infinite lexicographic product is not Noetherian either because is an infinite ascending chain.
• In this case " R " is also said to satisfy the ascending chain condition.
• An integral domain that satisfies the ascending chain conditions on divisorial ideals is called a Mori domain.
• The same equivalence holds for infinite lattices which satisfy the ascending chain condition ( or the descending chain condition ).
• A more algebraic way to see this is that the associated ideals defining algebraic sets must satisfy the ascending chain condition.
• Although the descending chain condition appears dual to the ascending chain condition, in rings it is in fact the stronger condition.
• The lattice of subgroups of a group satisfies the ascending chain condition if and only if all subgroups of the group are finitely generated.
• A collection of subsets of a given set satisfies the ascending chain condition if any ascending sequence becomes constant after a finite number of steps.
• One of the basic theorems in difference algebra asserts that every ascending chain of perfect difference ideals in K \ { y \ } is finite.
• Note that graded posets need not satisfy the ascending chain condition ( ACC ) : for instance, the natural numbers contain the infinite ascending chain 0.
• Note that graded posets need not satisfy the ascending chain condition ( ACC ) : for instance, the natural numbers contain the infinite ascending chain 0.
• A Noetherian module is a module which satisfies the ascending chain condition on submodules, that is, every increasing chain of submodules becomes stationary after finitely many steps.
• The collection \ mathcal { S } _ 2 of these subsets cannot contain an infinite ascending chain, so has a maximal element " F " 2.
• A finite lattice, or more generally a lattice satisfying the ascending chain condition or the descending chain condition, is semimodular if and only if it is M-symmetric.
• By Zorn's lemma, this is equivalent to saying that the ascending chain condition holds : there is no infinite strictly ascending chain of congruences on " S ".
• By Zorn's lemma, this is equivalent to saying that the ascending chain condition holds : there is no infinite strictly ascending chain of congruences on " S ".
• The subgroup generated by the normal locally nilpotent subgroups is called the Hirsch Plotkin radical and is the generalization of the Fitting subgroup to groups without the ascending chain condition on normal subgroups.
• In particular, Goldie's theorem applies to semiprime right Noetherian rings, since by definition right Noetherian rings have the ascending chain condition on " all " right ideals.